Complementary expressions for the scaling function near a magnetic critical point

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Abstract
Simple asymptotic expressions for the scaling functions, h(x)=x- phi 0)gamma valid near t=0, and x(h)=- mod h- psi 0-(t) mod 1 gamma / valid in a narrow region near H=O, t0 in a narrow region near hi=constant, where hi can be made arbitrarily close to infinity. An estimate Gamma +/ Gamma - approximately=( delta -1) for the ratio of inverse susceptibility amplitudes above and below Tc is obtained. Comparison of h(x) with very accurate recent data on Ni gives an excellent agreement which is at least as good as that obtained using an optimised set of linear parametric equations.